$L_p$–$L_q$ maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
Yoshihiro Shibata, Senjo Shimizu · Advanced studies in pure mathematics · 2019
We consider the Neumann problem for the Stokes equations with non-homogeneous boundary and divergence conditions in a bounded domain. We obtain a global in time $L_p$-$L_q$ maximal regularity theorem with exponential stability. To prove the $L_p$-$L_q$ maximal regularity, we use the Weis operator valued Fourier multiplier theorem.